What is the quantity dual to the Lagrangian density?

Abstract

We address the lately discovered Lagrangian density $\mathcal{L}$ of nonlinear electrodynamics preserving both conformal invariance and electric-magnetic duality to show that the quantity dual to $\mathcal{L}$ is $\mathcal{K}=\frac{1}{2}\sqrt{{\Theta }_{\mu \nu }{\Theta }^{\mu \nu }}$, where ${\Theta }_{\mu \nu }$ is the stress-energy tensor built out of this $\mathcal{L}$. We point out that $\mathcal{L}$ and $\mathcal{K}$ make up a pair of canonically conjugate variables which can be regarded as local coordinates of a two-dimensional symplectic manifold.

4 pages

Cited by in corpus (2)

• Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations
• Maximally symmetric nonlinear extension of electrodynamics and charged particles